Question

convergance of sum of Ln(n)/n

Answer 1

the sum diverges actually

Answer 2

so we would compare it to 1/n

Answer 3

yes, ln(n)/n > 1/n,

since 1/n diverges, by comparison test, ln(n)/n also diverges

Answer 4

ok so 1/n diverges by the harmonic series test

Answer 5

yea

Answer 6

can u explain tht pls

Answer 7

The comparison test states that, if an > bn for all natural n and sum (bn) diverges, then sum (an) diverges

Answer 8

is this the same thing for (ln(n))^2/n

Answer 9

cause (ln(n))^2 > 1^2

Answer 10

yes

Answer 11

kk thank u!

Answer 12

one minor point:

your inequality is not true for all natural numbers...so you should point out that

\[\ln(n)>1 \text{ for }n\ge3\]

which is all you need. you don't really care what happens at the beginning of the sequence, only what happens after a finite sequence of terms.